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This article presents a reduced-order model of the highly turbulent wind turbine wake dynamics. The model is derived using a large eddy simulation (LES) database, which cover a range of different wind speeds. The model consists of several sub-models: (1) dimensionality reduction using proper orthogonal decomposition (POD) on the global database, (2) projection in modal coordinates to get time series of the dynamics, (3) interpolation over the parameter space that enables the prediction of unseen cases, and (4) stochastic time series generation to generalize the modal dynamics based on spectral analysis. The model is validated against an unseen LES case in terms of the modal time series properties as well as turbine performance and aero-elastic responses. The reduced-order model provides LES accuracy and comparable distributions of all channels. Furthermore, the model provides substantial insights about the underlying flow physics, how these change with respect to the thrust coefficient CT, and whether the model is constructed for single wake or deep array conditions. The predictive and stochastic capabilities of the reduced-order model can effectively be viewed as a generalization of a LES for statistically stationary flows, and the model framework can be applied to other flow cases than wake dynamics behind wind turbines.

Wind farm flow control (WFFC) is a topic of interest at several research institutes and industry and certification agencies worldwide. For reliable performance assessment of the technology, the efficiency and the capability of the models applied to WFFC should be carefully evaluated. To address that, the FarmConners consortium has launched a common benchmark for code comparison under controlled operation to demonstrate its potential benefits, such as increased power production. The benchmark builds on available data sets from previous field campaigns, wind tunnel experiments, and high-fidelity simulations. Within that database, four blind tests are defined and 13 participants in total have submitted results for the analysis of single and multiple wakes under WFFC. Here, we present Part I of the FarmConners benchmark results, focusing on the blind tests with large-scale rotors. The observations and/or the model outcomes are evaluated via direct power comparisons at the upstream and downstream turbine(s), as well as the power gain at the wind farm level under wake steering control strategy. Additionally, wake loss reduction is also analysed to support the power performance comparison, where relevant. The majority of the participating models show good agreement with the observations or the reference high-fidelity simulations, especially for lower degrees of upstream misalignment and narrow wake sector. However, the benchmark clearly highlights the importance of the calibration procedure for control-oriented models. The potential effects of limited controlled operation data in calibration are particularly visible via frequent model mismatch for highly deflected wakes, as well as the power loss at the controlled turbine(s). In addition to the flow modelling, the sensitivity of the predicted WFFC benefits to the turbine representation and the implementation of the controller is also underlined. The FarmConners benchmark is the first of its kind to bring a wide variety of data sets, control settings, and model complexities for the (initial) assessment of farm flow control benefits. It forms an important basis for more detailed benchmarks in the future with extended control objectives to assess the true value of WFFC.

International audience; Previous research has revealed the need for a validation study that considers several wake quantities and code types so that decisions on the trade‐off between accuracy and computational cost can be well informed and appropriate to the intended application. In addition to guiding code choice and setup, rigorous model validation exercises are needed to identify weaknesses and strengths of specific models and guide future improvements. Here, we consider 13 approaches to simulating wakes observed with a nacelle‐mounted lidar at the Scaled Wind Technology Facility (SWiFT) under varying atmospheric conditions. We find that some of the main challenges in wind turbine wake modeling are related to simulating the inflow. In the neutral benchmark, model performance tracked as expected with model fidelity, with large‐eddy simulations performing the best. In the more challenging stable case, steady‐state Reynolds‐averaged Navier–Stokes simulations were found to outperform other model alternatives because they provide the ability to more easily prescribe noncanonical inflows and their low cost allows for simulations to be repeated as needed. Dynamic measurements were only available for the unstable benchmark at a single downstream distance. These dynamic analyses revealed that differences in the performance of time‐stepping models come largely from differences in wake meandering. This highlights the need for more validation exercises that take into account wake dynamics and are able to identify where these differences come from: mesh setup, inflow, turbulence models, or wake‐meandering parameterizations. In addition to model validation findings, we summarize lessons learned and provide recommendations for future benchmark exercises.

Wind turbines are designed to align themselves with the incoming wind direction. However, turbines often experience unintentional yaw misalignment, which can significantly reduce the power production. The unintentional yaw misalignment increases for turbines operating in the wake of upstream turbines. Here, the combined effects of wakes and yaw misalignment are investigated, with a focus on the resulting reduction in power production. A model is developed, which considers the trajectory of each turbine blade element as it passes through the wake inflow in order to determine a power–yaw loss exponent. The simple model is verified using the HAWC2 aeroelastic code, where wake flow fields have been generated using both medium- and high-fidelity computational fluid dynamics simulations. It is demonstrated that the spatial variation in the incoming wind field, due to the presence of wakes, plays a significant role in the power loss due to yaw misalignment. Results show that disregarding these effects on the power–yaw loss exponent can yield a 3.5 % overestimation in the power production of a turbine misaligned by 30∘. The presented analysis and model is relevant to low-fidelity wind farm optimization tools, which aim to capture the combined effects of wakes and yaw misalignment as well as the uncertainty on power output.

Wind farm flow control (WFFC) is a topic of interest at several research institutes, industry and certification agencies world-wide. For reliable performance assessment of the technology, the efficiency and the capability of the models applied to WFFC should be carefully evaluated. To address that, FarmConners consortium has launched a common benchmark for code comparison under controlled operation to demonstrate its potential benefits such as increased power production. The benchmark builds on available data sets from previous field campaigns, wind tunnel experiments and high-fidelity simulations. Within that database, 4 blind tests are defined and 13 participants in total have submitted results for the analysis of single and multiple wake under WFFC. Some participants took part in several blind tests and some participants have implemented several models. The observations and/or the model outcomes are evaluated via direct power comparisons at the upstream and downstream turbine(s), as well as the power gain at the wind farm level under wake steering control strategy. Additionally, wake loss reduction is also analysed to support the power performance comparison, where relevant. Majority of the participating models show good agreement with the observations or the reference high-fidelity simulations, especially for lower degrees of upstream misalignment and narrow wake sector. However, the benchmark clearly highlights the importance of the calibration procedure for control-oriented models. The potential effects of limited controlled operation data in calibration is particularly visible via frequent model mismatch for highly deflected wakes, as well as the power loss at the controlled turbine(s). In addition to the flow modelling, sensitivity of the predicted WFFC benefits to the turbine representation and the implementation of the controller is also underlined. FarmConners benchmark is the first of its kind to bring a wide variety of data sets, control settings and model complexities for the (initial) assessment of farm flow control benefits. It forms an important basis for more detailed benchmarks in the future with extended control objectives to assess the true value of WFFC.

A simple wind-speed-independent actuator disk control method is proposed that can be applied to speed up annual energy production calculations of wind farms using Reynolds-averaged Navier–Stokes simulations. The new control method allows the user to simulate the effect of different wind speeds in one simulation by scaling a calibrated thrust coefficient curve, while keeping the inflow constant. Since the global flow is not changed, only the local flow around the actuator disks need be recalculated from a previous converged result, which reduces the number of required iterations and computational effort by a factor of about 2–3.

Via 11 years of high-frequency measurements, we calculated the probability space of expected offshore wind-speed ramps, recasting it compactly in terms of relevant load-driving quantities for horizontal-axis wind turbines. A statistical ensemble of events in reduced ramp-parameter space (ramp acceleration, mean speed after ramp, upper-level shear) was created to capture the variability of ramp parameters and also allow connection of such to ramp-driven loads. Constrained Mann-model (CMM) turbulence simulations coupled to an aeroelastic model were made for each ensemble member, for a single turbine. Ramp acceleration was found to dominate the maxima of thrust-associated loads, with a ramp-induced increase of 45 %–50 % for blade-root flap-wise bending moment and tower-base fore–aft moment, plus ∼ 3 % per 0.1 m/s2 of bulk ramp-acceleration magnitude. The ensemble of ramp events from the CMM was also embedded in large-eddy simulation (LES) of a wind farm consisting of rows of nine turbines. The LES uses actuator-line modeling for the turbines and is coupled to the aeroelastic model. The LES results indicate that the ramps, and the mean acceleration associated with them, tend to persist through the farm. Depending on the ramp acceleration, ramps crossing rated speed lead to maximum loads, which are nearly constant for the third row and further downwind. Where rated power is not achieved, the loads primarily depend on wind speed; as mean winds weaken within the farm, ramps can again have U < Vrated. This leads to higher loads than pre-ramp conditions, with the distance where loads begin to increase depending on inflow Umax⁡ relative to Vrated. For the ramps considered here, the effect of turbulence on loads is found to be small relative to ramp amplitude that causes Vrated to be exceeded, but for ramps with Uafter < Vrated, the combination of ramp and turbulence can cause load maxima. The same sensitivity of loads to acceleration is found in both the CMM-aeroelastic simulations and the coupled LES.

Wind farm simulation tools are used for a multitude of purposes, including energy yield calculations, wind farm control optimization, layout optimization, structural load analysis, and many more. However, the vast majority of farm software either fails to capture the dynamic nature of both the flow and the turbine structural response or demands a high computational cost such as large-eddy simulations (LES). In this study, we present a new mid-fidelity aeroelastic wind farm simulation software, HAWC2Farm, which can perform dynamic wind farm computations at the same temporal and spatial resolution as LES using a fraction of the computational resources. Wind farm simulations are performed with wake steering, and statistics are verified with results from LES performed using Ellipsys3D.

A total of 18 high fidelity simulations of large wind farms have been performed by three different institutions using various inflow conditions and simulation setups. The setups differ in how the atmospheric turbulence, wind shear and wind turbine rotors are modelled, encompassing a wide range of commonly used modelling methods within the LES framework. Various turbine spacings, atmospheric turbulence intensity levels and incoming wind velocities are considered. The work performed is part of the International Energy Agency(IEA) wind task Wakebench, and is a continuation of previously published results on the subject. This work aims at providing a methodology for studying the general flow behavior in large wind farms in a systematic way. It seeks to investigate and further understand the global trends of wind farm performance, with a focus on variability. Parametric studies first map the effect of various parameters on large aligned wind farms, including wind turbine spacing, wind shear and atmospheric turbulence intensity. The results are then aggregated and compared to engineering models as well as LES results from other investigations to provide an overall picture of how much power can be extracted from large wind farms operating below rated level. The simple engineering models, although they cannot capture the variability features, capture the general trends well. Response surfaces are constructed based on the large amount of aggregated LES data corresponding to a wide range of large wind farm layouts. The response surfaces form a basis for mapping the inherently varying power characteristics inside very large wind farm, including how much the turbines are able to exploit the turbulent fluctuations within the wind farms and estimating the associated uncertainty, which is valuable information useful for risk mitigation.

This paper aims to develop fast and reliable surrogate models for yaw-based wind farm control. The surrogates, based on polynomial chaos expansion (PCE), are built using high-fidelity flow simulations coupled with aeroelastic simulations of the turbine performance and loads. Developing a model for wind farm control is a challenging control problem due to the time-varying dynamics of the wake. The wind farm control strategy is optimized for both the power output and the loading of the turbines. The optimization performed using two Vestas V27 turbines in a row for a specific atmospheric condition suggests that a power gain of almost 3%±1% can be achieved at close spacing by yawing the upstream turbine more than 15∘. At larger spacing the optimization shows that yawing is not beneficial as the optimization reverts to normal operation. Furthermore, it was also identified that a reduction in the equivalent loads was obtained at the cost of power production. The total power gains are discussed in relation to the associated model errors and the uncertainty of the surrogate models used in the optimization, as well as the implications for wind farm control.

Careful validation of the modelling and control actions is of vital importance to build confidence in the value of coordinated wind farm control (WFC). The efficiency of flow models applied to WFC should be evaluated to provide reliable assessment of the performance of WFC. In order to achieve that, FarmConners launches a common benchmark for code comparison to demonstrate the potential benefits of WFC, such as increased power production and mitigation of loads. The benchmark builds on available data sets from previous and ongoing campaigns: synthetic data from high-fidelity simulations, measurements from wind tunnel experiments, and field data from a real wind farm. The participating WFC models are first to be calibrated or trained using normal operation periods. For the blind test, both the axial induction and wake steering control approaches are included in the dataset and to be evaluated through the designed test cases. Three main test cases are specified, addressing the impact of WFC on single full wake, single partial wake, and multiple wake. The WFC model outcomes will be compared during the blind test phase, through power gain and wake loss reduction as well as alleviation of wake-added turbulence intensity and structural loads. The probabilistic validation will be based on the median and quartiles of the observations and WFC model predictions. Every benchmark participant will be involved in the final publication, where the comparison of different tools will be performed using the defined test cases. Instructions on how to participate are also provided on farmconners.readthedocs.io.

This paper presents a method for obtaining the free-inflow velocities from a 3-D flow sensor mounted on the blade of a wind turbine. From its position on the rotating blade, e.g. one-third from the tip, a blade-mounted flow sensor (BMFS) is able to provide valuable information about the turbulent sheared inflow in different regions of the rotor. At the rotor, however, the inflow is affected by the wind turbine, and in most cases the wind of interest is the inflow that the wind turbine is exposed to, i.e. the free-inflow velocities. The current method applies a combination of aerodynamic models and procedures to estimate the induced velocities, i.e. the disturbance of the flow field caused by the wind turbine. These velocities are subtracted from the flow velocities measured by the BMFS to obtain the free-inflow velocities. Aeroelastic codes, like HAWC2, typically use a similar approach to calculate the induction, but they use it for the reversed process, i.e. they add the induction to the free inflow to get the flow velocities at the blades, which are required to calculate the resulting aerodynamic forces. The aerodynamic models included in the current method comprise models based on blade element momentum (BEM) for axial and tangential induction, a radial induction model and tip loss correction, and models for skew and dynamic inflow. It is shown that the method is able to calculate the free-inflow velocities with high accuracy when applied to aeroelastic HAWC2 simulations with a stiff structural model while some deviations are seen in simulations with a flexible structure. Furthermore, the method is tested on simulations performed by a flexible structural model coupled with a large-eddy simulation (LES) flow solver. The results of this higher-fidelity verification confirm the HAWC2-based conclusion.

In this paper, we investigate the sound propagation from a wind turbine considering the effects of wake-induced velocity deficit and turbulence. In order to address this issue, an advanced approach was developed in which both scalar and vector parabolic equations in two dimensions are solved. Flow field input was obtained using the actuator line (AL) technique with Large Eddy Simulation (LES) to model the wind turbine and its wake and from an analytical wake model. The effect of incoming wind speed and atmospheric stability was investigated with the analytical wake input using a single point source. Unsteady acoustic simulations were carried out with the AL/LES input for three cases with different incoming turbulence intensity, and a moving source approach to mimic the rotating turbine blades. The results show a non-negligible effect of the wake on far-field noise prediction. Particularly under stable atmospheric conditions, SPL amplification reaches up to 7.5 dB at the wake centre. Furthermore, it was observed that when the turbulence intensity level of the incoming flow is higher, the SPL difference between the moving and the steady source is lower.

This paper aims to develop fast and reliable surrogate models for yaw-based wind farm control. The surrogates, based on polynomial chaos expansion (PCE), are built using high fidelity flow simulations combined with aeroelastic simulations of the turbine performance and loads. Developing a model for wind farm control is a challenging control problem due to the time-varying dynamics of the wake. Both the power output and the loading of the turbines are included in the optimization of wind farm control strategies. Optimization results performed using two Vestas V27 turbines in a row for a specific atmospheric condition suggest that a power gain of almost 3 % ± 1 % can be achieved at close spacing by yawing the upstream turbine more than 15°. At larger spacing, the power gain the optimization shows that yawing is not beneficial as the optimization reverts to normal operation. Furthermore, it was also identified that a reduction of the equivalent loads was obtained at the cost of power production. The total power gains are discussed in relation to the associated model errors and the uncertainty of the surrogate models used in the optimization, and the implication for wind farm control.

A simple wind speed independent actuator disk control method is proposed that can be applied to speed up annual energy production calculations of wind farms using Reynolds-averaged Navier–Stokes simulations. The new control method allows the user to simulate the effect of different wind speeds in one simulation by scaling a calibrated thrust coefficient curve, while keeping the inflow constant. Since the global flow is not changed, only the local flow around the actuator disks needs be recalculated from a previous converged result, which reduces the number of required iterations and computational effort by a factor of about 2–3.

Numerical simulations of the Vestas multi-rotor demonstrator (4R-V29) are compared with field measurements of power performance and remote sensing measurements of the wake deficit from a short-range WindScanner lidar system. The simulations predict a gain of 0 %–2 % in power due to the rotor interaction at below rated wind speeds. The power curve measurements also show that the rotor interaction increases the power performance below the rated wind speed by 1.8 %, which can result in a 1.5 % increase in the annual energy production. The wake measurements and numerical simulations show four distinct wake deficits in the near wake, which merge into a single-wake structure further downstream. Numerical simulations also show that the wake recovery distance of a simplified 4R-V29 wind turbine is 1.03–1.44 Deq shorter than for an equivalent single-rotor wind turbine with a rotor diameter Deq. In addition, the numerical simulations show that the added wake turbulence of the simplified 4R-V29 wind turbine is lower in the far wake compared with the equivalent single-rotor wind turbine. The faster wake recovery and lower far-wake turbulence of such a multi-rotor wind turbine has the potential to reduce the wind turbine spacing within a wind farm while providing the same production output.

Actuator disc and actuator line techniques are widely used for modelling wind turbines operating in wind farms. These techniques essentially replace the blade geometry with applied body forces, which reduce the resolved length scales significantly and hence the required grid resolution. This work is a verification of the coupling between the flow solver EllipSys3D and the aeroelastic tool Flex5, through a quantitative comparison of coupled actuator line, coupled actuator disc, and standalone Flex5. Steady state performance predictions, instantaneous reaction to turbulence and damage equivalent load analyses all show a very good agreement between the three methods. Differences can be explained primarily by the higher fidelity modelling of the coupled simulations; this is particularly in regard to the influence of blade flexibility, as the actuators deflect and interact with the modelled flow. Additionally, some overpredictions of loading at the blade tip and root below rated velocity for the actuator methods can be attributed to the Gaussian smearing used to apply the body forces.

Large eddy simulations of wind farms are often performed with canonical atmospheric conditions, where the background flow is based on precursor simulations with idealized model setups yielding statistically stationary turbulent flows. However, precursor simulations can only handle gradually changing flow conditions, and are not capable of modelling highly transient and statistically non-stationary flows, e.g. frontal passages or large gusts. Such flows frequently occur in nature, and can influence the operation—and potentially design—of wind turbines. It is generally not possible to impose non-stationary features through inlet boundary conditions, if the imposed flow violates the most fundamental assumption of micro-scale flow simulations, namely conservation of mass. This work presents a method for modelling highly transient wind speed ramps by extending and adapting the method of applying body forces to achieve specific flow scenarios, where the wind speed ramps are embedded as constrained turbulent boxes. Several scenarios with significant increases in the streamwise wind speed are simulated. Analyses of the transient wake dynamics, as the wind speed ramps propagate through large wind farms are performed to show how well the momentum is maintained throughout the numerical domain and the influence and operation of turbines during the ramp passages.

Wind farms experience significant efficiency losses due to the aerodynamic interaction between turbines. A possible control technique to minimize these losses is yaw-based wake steering. This paper investigates the potential for improved performance of the Lillgrund wind farm through a detailed calibration of a low-fidelity engineering model aimed specifically at yaw-based wake steering. The importance of each model parameter is assessed through a sensitivity analysis. This work shows that the model is overparameterized as at least one model parameter can be excluded from the calibration. The performance of the calibrated model is tested through an uncertainty analysis, which showed that the model has a significant bias but low uncertainty when comparing the predicted wake losses with measured wake losses. The model is used to optimize the annual energy production of the Lillgrund wind farm by determining yaw angles for specific inflow conditions. A significant energy gain is found when the optimal yaw angles are calculated deterministically. However, the energy gain decreases drastically when uncertainty in input conditions is included. More robust yaw angles can be obtained when the input uncertainty is taken into account during the optimization, which yields an energy gain of approximately 3.4%.

Loads from extreme waves can be dimensioning for the substructures of offshore wind turbines. The DeRisk project (2015-2019) aims at an improved load evaluation procedure for extreme waves through application of advanced wave models, laboratory tests of load effects, development of hydrodynamic load models, aero-elastic response calculations and statistical analysis. This first paper from the project outlines the content and philosophy behind DeRisk. Next, the first results from laboratory tests with irregular waves are presented, including results for 2D and 3D focused wave groups. The results of focused wave group tests and a 6-hour (full scale duration) test are reproduced numerically by re-application of the wave paddle signal in a fully nonlinear potential flow wave model. A good match for the free surface elevation and associated exceedance probability curve is obtained. Finally, the utilization of DeRisk's results in practical design is discussed.

In this paper we report the results of a workshop organised by the Delft University of Technology in 2014, aiming at the comparison between different state-of-the-art numerical models for the simulation of wind turbine wakes. The chosen benchmark case is a wind tunnel measurement, where stereoscopic Particle Image Velocimetry was employed to obtain the velocity field and turbulence statistics in the near wake of a two-bladed wind turbine model and of a porous disc, which mimics the numerical actuator used in the simulations. Researchers have been invited to simulate the experimental case based on the disc drag coefficient and the inflow characteristics. Four large eddy simulation (LES) codes from different institutions and a vortex model are part of the comparison. The purpose of this benchmark is to validate the numerical predictions of the flow field statistics in the near wake of an actuator disc, a case that is highly relevant for full wind farm applications. The comparison has shown that, despite its extreme simplicity, the vortex model is capable of reproducing the wake expansion and the centreline velocity with very high accuracy. Also all tested LES models are able to predict the velocity deficit in the very near wake well, contrary to what was expected from previous literature. However, the resolved velocity fluctuations in the LES are below the experimentally measured values.

People who pay their energy bills individually based on meter readings tend to spend less energy than people who pay collectively e.g. based on floor areas. It has been hypothesised that these savings are an effect of lower indoor temperatures and ventilation rates during heating seasons. The aim of this paper was to study the indoor environment in buildings with collective and individual heat cost allocation plans, to investigate how the heat cost allocation influenced occupant behaviour and how occupants controlled the indoor environment. The effects of the heat cost allocation type were studied by comparing indoor environmental measurements between two buildings: one with collective payment and one with individual payment. The measurements were collected at 5 min intervals at a central location in each of 56 apartments in Copenhagen, Denmark over a period of two months. Questionnaires and semi-structured interviews showed a strong influence of the heat cost allocation plan on the occupants' control strategies. Occupants whose heating bills were based on floor area focused on a healthy and comfortable indoor environment. Occupants whose heating bills were based on meter readings focused on energy conservation and heat cost savings at the expense of thermal comfort and air quality. The differences in average temperature, average CO2 concentration and average vapour pressure were 2.8 °C, 161 ppm, and 93 Pa, respectively between apartments with collective and individual heat cost allocation.

A new analytical model for representing body forces in numerical actuator disc models of wind turbines is compared to results from a BEM model. The model assumes the rotor disc being subject to a constant circulation, modified for tip and root effects. The advantage of the model is that it does not depend on any detailed knowledge concerning the actual wind turbine being analysed, but only requires information of the thrust coefficient and tip speed ratio. The model is validated for different turbines operating under a wide range of operating conditions. The comparisons show generally an excellent agreement with the BEM model, with, however, some deviations of the tangential force in the root area and at small values of the thrust coefficient.

For load calculations on wind turbines it is usually assumed that the turbulence approaching the rotor does not change its statistics as it goes through the induction zone. We investigate this assumption using a nacelle-mounted forward-looking pulsed lidar that measures low frequency wind fluctuations simultaneous at distances between one half and three rotor diameters upstream. The measurements show that below rated wind speed the low-frequency wind variance is reduced by up to 10 % at one half rotor diameter upstream and above rated enhanced by up to 20 %. A quasi-steady model that takes into account the change of thrust coefficient with wind speed explains these variations partly. Large-eddy simulations of turbulence approaching an actuator disk model of a rotor support the finding that the slope of the thrust curve influences the low-frequency fluctuations.

On 25 January 2016 at 12:45 UTC several photographs of the offshore wind farm Horns Rev 2 were taken by helicopter pilot Gitte Lundorff with an iPhone. A very shallow layer of fog covered the sea. The photos of the fog over the seadramatically pictured the offshore wind farm wake. Researchers got together to investigate the atmospheric conditions at the time of the photos by analysing local meteorological observations and wind turbine information, satellite remotesensing and nearby radiosonde data. Two wake models and one mesoscale model were used to model the case and explain what was seen.

Offshore wind farm wakes were observed and photographed in foggy conditions at Horns Rev 2 on 25 January 2016 at 12:45 UTC. These new images show highly contrasting conditions regarding the wind speed, turbulence intensity, atmospheric stability, weather conditions and wind farm wake development as compared to the Horns Rev 1 photographs from 12 February 2008. The paper examines the atmospheric conditions from satellite images, radiosondes, lidar and wind turbine data and compares the observations to results from atmospheric meso-scale modelling and large eddy simulation. Key findings are that a humid and warm air mass was advected from the southwest over cold sea and the dew-point temperature was such that cold-water advection fog formed in a shallow layer. The flow was stably stratified and the freestream wind speed was 13 m/s at hub height, which means that most turbines produced at or near rated power. The wind direction was southwesterly and long, narrow wakes persisted several rotor diameters downwind of the wind turbines. Eventually mixing of warm air from aloft dispersed the fog in the far wake region of the wind farm.

In the present work, an in-house UnSteady Double Wake Model (USDWM) is developed for simulating general flow problems behind bodies. The model is presented and used to simulate flows past a circular cylinder at subcritical, supercritical, and transcritical flows. The flow model is a two-dimensional panel method which uses the unsteady double wake technique to model flow separation and its dynamics. In the present work the separation location is obtained from experimental data and fixed in time. The highly unsteady flow field behind the cylinder is analyzed in detail. The results are compared with experiments and Unsteady Reynolds-Averaged Navier Stokes (URANS) simulations and show good agreement in terms of the vortex shedding characteristics, drag, and pressure coefficients for the different flow regimes.

The turbulence in the interior of a wind farm is simulated using large eddy simulation and the actuator line technique implemented in the Navier–Stokes equations. The simulations are carried out for an infinitely long row of turbines simulated by applying cyclic boundary conditions at the inlet and outlet. The simulations investigate the turbulence inherent to the wind turbines as no ambient turbulence or shear is added to this idealised case. The simulated data give insight into the performance of the wind turbines operating in the wake of others as well as details on key turbulent quantities. One of the key features of wakes behind wind turbines is the dynamic wake meandering, which is shown to be related to the wind turbine spacing and the vortex shedding from the turbine as a bluff body. The flow is analysed and reconstructed by applying proper orthogonal decomposition.

In the present work, the in-house UnSteady Double Wake Model (USDWM) is used to simulate flows past a cylinder at subcritical, supercritical, and transcritical Reynolds numbers. The flow model is a two-dimensional panel method which uses the unsteady double wake technique to model flow separation and its dynamics. In the present work the separation location is obtained from experimental data and fixed in time. The highly unsteady flow field behind the cylinder is analyzed in detail, comparing the vortex shedding charactericts under the different flow conditions.

Ten simulations of large wind farms have been performed using a fully coupled LES and aero-elastic framework to form a database of full turbine operational conditions in terms of both production and loads. The performance is examined in terms of averaged power production and thrust, as well as 10min equivalent flapwise bending, yaw, and tilt moment loads. Certain scenarios operating below rated wind speed shows unexpected peaks in the loads. The influence on the operating conditions are examined for various parameters and compared relative to an effective power production per area.

A number of large wind farms are modelled using large eddy simulations to elucidate the entrainment process. A reference simulation without turbines and three farm simulations with different degrees of imposed atmospheric turbulence are presented. The entrainment process is assessed using proper orthogonal decomposition, which is employed to detect the largest and most energetic coherent turbulent structures. The dominant length scales responsible for the entrainment process are shown to grow further into the wind farm, but to be limited in extent by the streamwise turbine spacing, which could be taken into account when developing farm layouts. The self-organized motion or large coherent structures also yield high correlations between the power productions of consecutive turbines, which can be exploited through dynamic farm control. This article is part of the themed issue ‘Wind energy in complex terrains’.

Numerous large eddy simulations are performed of large wind farms using the actuator line method, which has been fully coupled to the aero-elastic code, Flex5. The higher order moments of the flow field inside large wind farms is examined in order to determine a representative reference velocity. The statistical moments appear to collapse and hence the turbulence inside large wind farms can potentially be scaled accordingly. The thrust coefficient is estimated by two different reference velocities and the generic C-T expression by Frandsen. A reference velocity derived from the power production is shown to give very good agreement and furthermore enables the very good estimation of the thrust force using only the steady C-T-curve, even for very short time samples. Finally, the effective turbulence inside large wind farms and the equivalent loads are examined.

Wind turbine sound generation and propagation phenomena are inherently time dependent, hence tools that incorporate the dynamic nature of these two issues are needed for accurate modelling. In this paper, we investigate the sound propagation from a wind turbine by considering the effects of unsteady flow around it and time dependent source characteristics. For the acoustics modelling we employ the Parabolic Equation (PE) method while Large Eddy Simulation (LES) as well as synthetically generated turbulence fields are used to generate the medium flow upon which sound propagates. Unsteady acoustic simulations are carried out for three incoming wind shear and various turbulence intensities, using a moving source approach to mimic the rotating turbine blades. The focus of the present paper is to study the near and far field amplitude modulation characteristics and time evolution of Sound Pressure Level (SPL).

The wind turbine design standards recommend two different methods to generate turbulent wind for design load analysis, the Kaimal spectra combined with an exponential coherence function and the Mann turbulence model. The two turbulence models can give very different estimates of fatigue life, especially for offshore floating wind turbines. In this study the spatial distributions of the two turbulence models are investigated using Proper Orthogonal Decomposition, which is used to characterize large coherent structures. The main focus has been on the structures that contain the most energy, which are the lowest POD modes. The Mann turbulence model generates coherent structures that stretches in the horizontal direction for the longitudinal component, while the structures found in the Kaimal model are more random in their shape. These differences in the coherent structures at lower frequencies for the two turbulence models can be the reason for differences in fatigue life estimates for wind turbines.

Large Eddy Simulations are inherently dynamic as the largest scales are resolved and the smallest scales are modeled temporally. This raises challenges for simulations including very large scales such as atmospheric flows, which require very long simulation times. Simple averages fail at capturing these dynamics and potentially yield misleading interpretations concerning the capabilities of different models when tested in blind tests or in benchmarking exercises such as Wakebench, where results from different flow models are compared. This article will present results from very large wind farm simulations using Actuator Disc (AD) and Line (AL) models for two different turbine spacings with turbulent inflow. The results of each numerical flow model include a certain variability, and it will be examined if different models result in comparable probability distributions.

The actuator line technique was introduced as a numerical tool to be employed in combination with large eddy simulations to enable the study of wakes and wake interaction in wind farms. The technique is today largely used for studying basic features of wakes as well as for making performance predictions of wind farms. In this paper, we give a short introduction to the wake problem and the actuator line methodology and present a study in which the technique is employed to determine the near-wake properties of wind turbines. The presented results include a comparison of experimental results of the wake characteristics of the flow around a three-bladed model wind turbine, the development of a simple analytical formula for determining the near-wake length behind a wind turbine and a detailed investigation of wake structures based on proper orthogonal decomposition analysis of numerically generated snapshots of the wake.

The turbulence in the interior of an idealised wind farm is simulated using Large Eddy Simulation and the Actuator Line technique implemented in the Navier-Stokes equations. The simulation is carried out for an 'infinitely' long row of turbines simulated by applying cyclic boundary conditions at the inlet and outlet. The simulations investigate the turbulence inherent to the wind turbines as no ambient turbulence or shear is added to this idealised case. A Reduced Order Model for the highly turbulent flow deep inside a wind farm is proposed based on a Proper Orthogonal Decomposition. The reconstructed flow is shown to capture the large scale motions of the highly turbulent flow.

Experimental stereoscopic PIV measurements in the wake of a two-bladed rotor and a porous actuator disc are compared to numerical simulation of an actuator disc. Compared to previous literature, the focus of the present analysis is on the near wake, where the actuator discs fail to represent the complex flow structures correctly, which affects the downstream representation of the full wake behind a real rotor. The near wake region is characterised by the instability and breakdown of the tip-vortex helical system, which constitutes the onset of a stronger mixing process. The comparison focuses on the turbulent structures in the shear layer at the borders of the wake through the analysis of the Reynolds stresses and by employing POD on two separate regions. The analysis shows that the actuator discs fail to capture the details of the complex flow behind a rotor, but that the experimental and numerical actuator discs are generally comparable at a certain distance behind the actuator disc. This project is intended to provide the basis for understanding the origin of the limitations of the current wake models based on the actuator disc assumption.

As part of a study of energy retrofits in nine California buildings indoor measurements of temperature and relative humidity were made between 2010 and 2012. The aim of this paper was to compare the temperature and relative humidity measurements in relation to recommendations for a healthy, comfortable and low energy consuming indoor environment. Energy conserving behavior during the heating season was detected in all buildings. The paper further aimed to find patterns in the measurement to determine if an energy retrofit affects the occupants’ behavior and indoor environmental regulation strategies. No general pattern could be defined.

The Dynamic Wake Meandering model(DWM) by Larsen et al.(2007) is considered state of the art for modelling the wake behind a wind turbine. DWM assumes a quasi-steady wake deficit transported as a passive tracer by large atmospheric scales. The approach is also applied to wake interaction within wind farms, although certain aspects of the complex wake interaction are not captured, see Churchfield et al.(2014). Recent studies have shown how turbines introduce low frequencies in the wake, which could describe some of the shortcomings. Chamorro et al.(2015) identified three regions of different lengths scales. Iungo et al.(2013) related low frequencies to the hub vortex instability. Okulov et al.(2014) found Strouhal numbers in the far wake stemming from the rotating helical vortex core. Simulations by Andersen et al.(2013) found low frequencies to be inherent in the flow inside an infinite wind farm. LES simulations of large wind farms are performed with full aero-elastic Actuator Lines. The simulations investigate the inherent dynamics inside wind farms in the absence of atmospheric turbulence compared to cases with atmospheric turbulence. Resulting low frequency structures are inherent in wind farms for certain turbine spacings and affect both power production and loads.